Question

Determine the set of values of k for the given quadratic equation has real roots:

kx² + 6x + 1 = 0

Answer 1

Given,

2x² + x + k = 0

It’s of the form of ax² + bx + c = 0

Where, a = 2, b = 1, c = k

For the given quadratic equation to have real roots D = b² – 4ac ≥ 0

D = 1² – 4(2)(k) ≥ 0

⇒ 1 – 8k ≥ 0

⇒ k ≤ \(\frac{1}{8}\)

The value of k should not exceed \(\frac{1}{8}\) to have real roots.